Conformal Field Theory as Microscopic Dynamics of Incompressible Euler and Navier-Stokes Equations

TL;DR

This paper demonstrates that the incompressible Euler and Navier-Stokes equations can be derived as limits of relativistic conformal field theories' hydrodynamics, offering a microscopic foundation for these classical fluid equations.

Contribution

It establishes a connection between conformal field theories and classical fluid dynamics, providing a microscopic basis for the Euler and Navier-Stokes equations.

Findings

Incompressible Euler equations emerge from ideal hydrodynamics of conformal field theories.

Incompressible Navier-Stokes equations arise from viscous hydrodynamics of conformal field theories.

Conformal field theories offer a fundamental microscopic perspective on fluid dynamics.

Abstract

We consider the hydrodynamics of relativistic conformal field theories at finite temperature. We show that the limit of slow motions of the ideal hydrodynamics leads to the non-relativistic incompressible Euler equation. For viscous hydrodynamics we show that the limit of slow motions leads to the non-relativistic incompressible Navier-Stokes equation. We explain the physical reasons for the reduction and discuss the implications. We propose that conformal field theories provide a fundamental microscopic viewpoint of the equations and the dynamics governed by them.